apoorva javadekar -role of reputation for mutual fund flows

Role of Reputation For Mutual Fund Flows

Apoorva Javadekar1

September 2, 2015

1 Boston University, Department of Economics

Broad Question

1. Question:What causes investors to invest or withdraw money from mutual funds?

) In particular: what is the link between fund performance and fund flows?

2. Litarature:Narrow focus on ”Winner Chasing” phenomenon

) link between recent-most performance and fund flows ignoring role for reputation of fund

3. This paper: Role of Fund Reputation) Investor’s choices) Risk Choices by fund managers

Why Study Fund Flows?1. Important Vehicle of Investment

) Large: Manage 15 Tr $ (ICI, 2014)) Dominant way to equities: (ICI -2014, French (2008))

) HH through MF: owns 30% US equities) Direct holdings of HH: 20% of US equities

) Participation: 46% of US HH invest

2. Understand Behavioral Patterns:) Investors learn about managerial ability through returns) =⇒ fund flows shed light on learning, information processing

capacities etc.

3. Fund Flows Affect Managerial Risk Taking) Compensation ≈ flows: 90% MF managers paid as a % of

=⇒ flow patterns can affect risk taking=⇒ impacts on asset prices

Literature Snapshot

1. Seminal Paper: Chevallier & Ellison (JPE, 1997)

Flows(t+1)

Returns(t)

=⇒ Convex Fund Flows in Recent Performance!

2. Why Interesting? Non-Linear Flows (could) mean

) Bad and extremely bad returns carry same information !) Non-Bayesian Learning) Behavioral Biases) Excess risk taking by managers given limited downside

Motivating Role of Reputation1. No Role For Reputation: Literature links time t returns (rit )

to time t + 1 fund flows (FF i , t+1)2. Why a Problem? The way investor perceives current

performance depends upon historic performance

Why? History of Returns ≈ reputation

Manager 1: {rt−3, rt−2, rt−1, rt} = {G, G, G, B}Manager 2: {rt−3, rt−2, rt−1, rt} = {B, B, B, B}

3. What it means for estimation?

FFi ,t+1 = g (rit, ri,t−1, ...) + errori,t+1

where g(.) is non-separable in returns4. Useful For Studying Investors Learning

FFi ,t+1 = g (

¸c¸isio

=ss¸ig

¸r¸io

rit , ri,t−1, ri,t−2, ...)

1. Source: CRSP Survivor-Bias free mutual fund dataset 2. Time Period: 1980-2012.3. Include:

) Domestic, Open ended, equity funds) Growth, Income, Growth&Income, Small and Mid-Cap, Capital

Appreciation funds (Pastor, Stambaugh (2002))4. Exclude

) Sectoral, global and index or annuity funds) Funds with sales restrictions) young funds with less than 5 years) small funds (Assets < 10 Mn $)

5. Annual Frequency: Disclosures of yearly returns, ratings are based on annual performance

Performance Measures1. Reputation: Aggregate performance of 3 or 5 years prior to

current period2. How to Measure Performance?

) Factor Adjusted: CAPM α or 3-factor α (Fama,French (2010), Kosowski (2006))

) Peer Ranking (Within each investment style):(Chevallier,Ellison (1997), Spiegel (2012))

3. Which Measure?) Not easy for naive investor to exploit factors like value,

premium or momentum =⇒ factor-mimicking is valued (Berk, Binsbergen (2013))

) Flows more sensitive to raw returns (Clifford (2011))) Peer ranking within each style control for bulk of risk

differentials across funds) CAPM α wins the horse race amongst factor models

(Barberet.al 2014)

4.I use both the measures: CAPM α and Peer Ranking but not 3-factor model.

Main Variables

1. Fund Flows: Main dependent variable is % growth in Assets due to fund flows

FFi,t+1 =Ai,t+1 − (A it × (1 + ri,t+1))

A i t : Assets with fund i at time t rit : Fund returns for period ended t

Empirical Methodology

FF i ,t +1

1. Interact Reputation With Recent Performance: To understand how investors mix signals with priors

k=1= β0 + .

i ,t −1

(rankit ).

k=1+ .

i ,t −1 × (rankit )2

. + controls +

εi,t+12. Variables:

Z ki ,t −1: Dummy for reputation category (k ) at t −

1) rankit ∈ [0, 1]

3. Structure:) Capture learning technology) No independent effects of reputation(t-1) on flows(t+1):

) Reputation affect flows only through posteriors

Results 1: OLS EstimationTable:Reputation And Fund Flows

Only Short Term Reputation

Dep Var:FFit+1 Peer CAPM Peer CAPM

Time Effects Yes Yes Yes YesStandard Errors Fund Clustered Fund Clustered Fund Clustered Fund Clustered

N 13512 13512 11468 11468Adj R-sq 0.137 0.135 0.158 0.148

Constant -0.088*** -0.109***(0.021) (0.021)

-0.098*** -0.126***(0.022) (0.022)

Rank(t+1) 0.216*** 0.202***(0.010) (0.010)

0.207*** 0.193***(0.011) (0.011)

Risk(t) -0.894*** -0.808***(0.183) (0.178)

-0.830*** -0.761***(0.193) (0.188)

Log Age (t) -0.031*** -0.027*** -0.010 -0.006(0.005) (0.005) (0.005) (0.005)

Log Size(t) -0.002 -0.002 -0.011*** -0.008***(0.001) (0.001) (0.001) (0.001)

∆ Style(t+1) 0.045 0.039 0.039 0.035(0.049) (0.038) (0.038) (0.033)

FFit +1Peer CAPM Peer CAPM

Unconditional Estimates

Rank(t) 0.043 0.117**(0.041) (0.041)

Rank-Sq(t) 0.296*** 0.223***(0.043) (0.043)

Low Reputation (Bottom 20%)

Rank(t) -0.031 -0.031(0.054) (0.060)

Rank-Sq(t) 0.210*** 0.250***(0.062) (0.074)

Medium Reputation (Middle 60 %)

Rank(t) -0.023 0.077(0.046) (0.044)

Rank-Sq(t) 0.374*** 0.260***(0.052) (0.049)

Top Reputation (Top 20%)

Rank(t) 0.308*** 0.285***(0.059) (0.061)

Rank-Sq(t) 0.116 0.124-0.0693 -0.0741

Mean Estimates Graph

0 .5 1 0 1 0 .5 1

95% Confidence Interval Mean Flow Growth%(t+1)

Rank (t)

Flow Sensitivities In Response to ReputationLow reputation (t-1) Med reputation (t-1) Top Reputation(t-1)

Unconditional Estimates

0 .2 .4 .6 .8 1Rank(t)

95 % Confidence Interval Flow Growth % (t+1)

) %Short Term Performance And Flow Growth

Mean Estimates Graph

0 .5 1 0 1 0 .5 1

95% Confidence Interval Mean Flow Growth%(t+1)

Rank (t)

Flow Sensitivities In Response to ReputationLow reputation (t-1) Med reputation (t-1) Top Reputation(t-1)

Piecewise Linear Specification

0 .5 1 0 1 0 .5 1

95 % CI Flow Growth %

Rank ( t)

Reputation And Fund Flows (Piecewise Linear)Low Reputation Medium Reputation Top Reputation

Implications

1. Shape:) Convex Fund Flows For Low Reputation) Linear Flows for Top Reputation

2. Level:) Flows% increasing in reputation for a given short-term rank

) Break Even Rank: 0.90 for Low reputation funds Vs 0.40 for Top repute funds

3. Slope:) Flow sensitivity is lower for low reputation, even at the extreme

high end of current performance.

Robustness Checks

1. Reputation: 3 or 5 or 7 years of history2. Performance Measure: CAPM or Peer Ranks3. Standard Errors:

) Clustered SE (cluster by fund) with time effects controlled using time dummies

) Cluster by fund-year (Veldkamp et.al (2014))

4. Institutional Vs Individual Investors5. Fixed Effects Model: To control for fund family effects

Robustness With Fixed EffectsOnly Short Term Reputation

Dep Var:FFit+1 Peer CAPM Peer CAPM

Unconditional EstimatesRank(t) 0.0345

0.0871*(0.0435) (0.0430)

Rank-Sq(t) 0.276*** 0.232***(0.0453) (0.0448)

Low ReputationRank(t) -0.0978 -0.140*

(0.0592) (0.0630)

Rank-Sq(t) 0.244*** 0.339***(0.0682) (0.0776)

Medium ReputationRank(t) -0.0566 0.0270

(0.0496) (0.0491)

Rank-Sq(t) 0.389*** 0.308***(0.0553) (0.0542)

Top ReputationRank(t) 0.323*** 0.359***

(0.0585) (0.0585)

Rank-Sq(t) 0.100 0.0528(0.0671) (0.0691)

Section II:

Risk Shifting

Evidence on Risk Shifting: Background1. Do mid-year losing funds change portfolio risk?

) Convex flows =⇒ limited downside in payoff

2. Previous Papers:

) Brown, Harlow, Starks (1996): Mid-Year losing funds increase the portfolio volatility

) Chevallier, Ellison (1997): marginal mid-year winners benchmark but marginal losers ↑ σ

) Busse (2001):) Uses daily data =⇒ efficient estimates of σ) No support for ∆σ(r i t )

) Basak(2007):) What is risk? σ or deviation from

benchmark/peers?) Shows that mid-year losers deviate from

benchmark) Portfolio risk can be up or down (σ ↓ or ↑)

3. But Flows Are Not Convex For All Funds !

Measuring Risk Shifting1.Consider a simplest factor model

R i t = αi + mtβi

lo¸a¸dx

=sp¸r¸ic

× R + s

2. Fact: Factors (e.g market) explain substantial σ(rit )

3. σ(rit ) Flawed meaure: Lot of exogenous variation for manager

4. Factor Loadings (β): Within manager control =⇒ good measure of risk-shifting

5. Measure of Devitation:

∆Risk = | βi,2ts¸¸xβ for 2nd half

− s¸¸xβ2t

median β for 2nd half

) Median β for funds with same investment style

Some StatisticsTable:Summary Statistics For Risk Change

Reputation Category

Variables Low Med Top

Annual BetaMean 1.04 1.02 1.02

Median 1.03 1.00 1.00Dispersion 0.19 0.15 0.20

∆ RiskMean 0.12 0.09 0.12

Median 0.084 0.066 0.091Dispersion 0.14 0.09 0.11

First Pass: Polynomial Smooth

Regression ResultsTable:Risk Shifting

Unconditional Control For ReputationDep: Beta Devitation Peer CAPM Peer CAPM

Time Effects Yes Yes Yes YesStyle Effects Yes Yes Yes Yes

Standard Errors Fund Clustered Fund Clustered Fund Clustered Fund Clustered

Constant 0.298*** (0.015)

0.291*** (0.015)

0.304*** (0.015)

0.305*** (0.016)

∆Risk Rank (H1) 0.542*** (0.008)

0.543*** (0.008)

0.534*** (0.008)

0.532*** (0.008)

Log Age(t) -0.007 -0.007 -0.006 -0.006(0.004) (0.004) (0.004) (0.004)

Log Size(t) -0.000 -0.000 -0.000 -0.002(0.001) (0.001) (0.001) (0.001)

Unconditional Beta Deviation

Perf. Rank(H1) -0.243*** -0.228***(0.029) (0.029)

Perf. Rank(H1)2 0.229*** 0.226***(0.028) (0.028)

Result ContinuedPeer CAPM

PeerCAPM

Low Reputation(t)

Perf. Rank(H1) -0.355*** -0.378***(0.042) (0.043)

Perf. Rank(H1)2 0.377*** 0.410***(0.048) (0.049)

Medium Reputation(t)

Perf. Rank(H1) -0.250*** -0.227***(0.032) (0.034)

Perf. Rank(H1)2 0.219*** 0.208***(0.033) (0.034)

Top Reputation(t)

Perf. Rank(H1) -0.0573 -0.0472(0.042) (0.043)

Perf. Rank(H1)2 0.034 0.044(0.046) (0.047)

Observations 15720 15720 14434 13406

Adj. R2 0.308 0.308 0.306 0.304

Mean Estimates For Risk-Shift

Discussion of Results

1. Low Reputation Funds) Severe career concerns

) Low Mid-Year Rank: Gamble for resurrection

) High Mid-Year Rank: Exploit convexity of flows as risk of job-loss relatively low

2. Top Reputation Funds:) No immediate career concerns =⇒ Level of deviation slightly

higher

) Flows Linear =⇒ No response to mid-year rank

Section III

Model Of Fund Flows

Model Overview

1. Question: What explains the heterogeniety in observed Fund-Flow schedules

2. Possible Answer:) Investor-Base is heterogenous for funds with different

reputation or track record.

3. Basic Intuition:) A model with loss-averse investors + partial visibility

) Rational investors shift out of poor perfoming funds but loss-averse agents stick

=⇒ Bad fund performs poor again: No outflows

=⇒ Poor fund perform Good: Some inflows as fund becomes ’visible’

Model Outline

1. Basic Set-Up:) Finite horizon model with T < ∞) Two mutual funds indexed by i = 1, 2) Two types of investors (N of each type)

) Rational Investors (R): 1 unit at t = 0) Loss-Averse Investors (B): has η units at t = 0

22. At t = 0: Each fund has N of each type of investors3. Partial Visibility:

) Fund is visible to fund insiders at year end

) Fund visibility at t to outsiders increases with performance at time t

) visible =⇒ entire history is known

Returns and Beliefs1. Return Dynamics:

ri,t+1 = αi + εit+1

εit+1 ∼ N .0, (σε)2 .

where αi = unobserved ability of manager

2. Beliefs:) I i t = Set of investors to whom i is visible) For every j ∈ I i t , priors at end of t are

i tα ∼ N αit tˆ , (σ )2. .

) All investors are Bayesian =⇒ Normal Posteriors with

αit+1 αit i ,t +1 αitˆ = ˆ + (r − ˆ ) (σt )

2t ε(σ )2 + (σ )2

Loss-Averse Investors1. Assumptions:

) Invest in only one of the visible funds at a time) Solves Two period problem every t as if model ends at t + 1

2. Preferences: Following Barberis, Xiong (2009)) πt = accumulated loss/gain for investor of B type with i) Instantaneous Utility realized only upon liquidation

u (πt ) =.δπ t 1 (πt < 0) + πt 1 (πt ≥ 0) If sell0 If no sell

) Evolution of πtπt+1 + ri,t+1πt +1 =

rj ,t +1 0

If no sellIf shift to fund j ∈ I i

If exit from industry

3. Trade-off: =⇒ B can mark-to-market loss today and exit fund i or carry forward losses in hope that rit+1 is large enough

4. Why? Loss hurts more: δ > 1

Motivation For Loss-Averse Investors

1. Strong Empirical Support:) Shefrin, Statman (1985), Odean(1998): Investors hold on

to losses for long but realize gains early) Calvet,Cambell, Sodini(2009): Slightly weaker but robust

tendency to hold on losing mutual funds) Heath (1999): Disposition effect present in ESOP’s

) Brown (2006), Frazzini (2006): Institutional traders exhibit tendency to hold losing investments

2. Why Realized Loss-Aversion?) Barberis, Xiong (2009): Realization Loss Averse preferences

can generate disposition effect

) Usual Prospect utility preferences over terminal gain/loss need not generate tendency to hold losses

Problem of Loss-Averse InvestorKeep Vs Sell Decision: B type invested in fund i = 1

t itV π , {α } ˆ i

. . ,t t= max V , V ,

Vsell keep

exit t

. . ,t t= max V , V ,

Vsell keep

exit t

In turn

α , π ) = E [u (π + r α1t

) | ˆ ]

t itV π , { ˆ }

i =1,2

. . ,t tα = max V , V ,

Vsell keep

exit t

In turn

α , π ) = E [u (π + r α1t

) | ˆ ]= P (πt + r1t+1 ≥ 0) E t [πt + r1t+1|πt + r1t+1 ≥ 0]

. . ,t t= max V , V ,

Vsell keep

exit t

In turn

α , π ) = E [u (π + r α1t

) | ˆ ]= P (πt + r1t+1 ≥ 0) E t [πt + r1t+1|πt + r1t+1 ≥ 0]

+P (πt + r1t+1 < 0) δEt [πt + r1t+1|πt + r1t+1 < 0]

. . ,t t= max V , V ,

Vsell keep

exit t

E [u (π + r α1t

) | ˆ ]

In turn

α , π ) == P (πt + r1t+1 ≥ 0) E t [πt + r1t+1|πt + r1t+1 ≥ 0]

t α1t= Q (π + ˆ )

tV π , {

it i =1,2

. . ,t t

α } = max V , V , V̂ sell keep

exit t

α1t) | ˆ ]

In turn

α , π ) = E [u (π + r

=P (πt + r1t+1 ≥ 0) E t [πt + r1t+1|πt + r1t+1 ≥ 0]

t α1t= Q (π + ˆ )

sellt α2t

tV (π , ˆ ) = u (π ) + E [u (r t 2t+1 α2t

) | ˆ ]

. . ,t t= max V , V ,

Vsell keep

exit t

α1t) | ˆ ]

In turn

α , π ) = E [u (π + r

t α1t= Q (π + ˆ )

sellt α2t

tV (π , ˆ ) = u (π ) + E [u (r t 2t+1 α2t

) | ˆ ]

. . ,t t= max V , V ,

Vsell keep

exit t

α1t) | ˆ ]

In turn

α , π ) = E [u (π + r

t α1t= Q (π + ˆ )

sellt α2t

tV (π , ˆ ) = u (π ) + E [u (r t 2t+1 α2t

) | ˆ ]= u (πt ) + P (r2t+1 ≥ 0) E t [r2t+1|r2t+1 ≥ 0]

tV π , {

it i =1,2

. . ,t t

α } = max V , V , V̂ sell keep

exit t

α1t) | ˆ ]

In turn

α , π ) = E [u (π + r

t α1t= Q (π + ˆ )

sellt α2t

tV (π , ˆ ) = u (π ) + E [u (r t 2t+1 α2t

) | ˆ ]= u (πt ) + P (r2t+1 ≥ 0) E t [r2t+1|r2t+1 ≥ 0]

+δP (r2t+1 < 0) E t [r2t+1|r2t+1 < 0]

. . ,t t= max V , V ,

Vsell keep

exit t

α1t) | ˆ ]

In turn

α , π ) = E [u (π + r

t α1t= Q (π + ˆ )

sellt α2t

tu (π ) + E [u (r t 2t+1 α2t

) | ˆ ]V (π , ˆ ) == u (πt ) + P (r2t+1 ≥ 0) E t [r2t+1|r2t+1 ≥

0]+δP (r2t+1 < 0) E t [r2t+1|r2t+1 < 0]t α2t

= u(π ) + Q ( ˆ )

Properties of Q(µ)

1.Expression for Q(µ), µ ∈ R

Q (µ) = µ + (δ − 1) .µΦ

.−µ .

− σφ .

µ . .

2. Q(µ) is increasing in µ. In particular, one unit rise in µchanges Q(µ) by more than 1 unit∂Q (µ)

µ ∂µσ

= 1 + (δ − 1) Φ .−

(1, δ)3. Q(µ) is concave, with

limµ→∞

∂µ∂Q(µ) = 1

∂2Q (µ)∂µ2

= −(δ − 1) σ

. µ .φ −σ < 0

Optimal Policy For Loss Averse Investor1. Result 1: Participation Premium

) t α1tFor any π , liquidation of current fund is optimal if ˆ < 0.

) In fact, break-even skill is positive. That is ifVkeep (α1,min(πt ), πt ) = Vexit (πt ), then α1,min(πt ) > 0, for anyπt

) Similarly, break-even level for manager 2 skill α2,min > 0. Else B will exit but not shift to fund 2

2. How to interpret ”LOW reputation then?) Relative: Low relative to Top, but still with positive expected

excess returns.

) Replacement Theory: Bad managers are replaced or bad funds merge with good funds. Hence expectation about ”fund returns” never go negative (e.g Lynch,Musto 2003)

α2t α1t t3. Assumption: ˆ > α and ˆ (π ) > α

2,min2,min

t(π )

Optimal Policy For Loss-Averse Investor1. Result 2: Hold Losses Unless Fund is Extremely Bad

)α2t α1t

α1t α2tIf Q ( ˆ ) < δ ˆ , then B holds if π < π ( ˆ , ˆ ), for some∗

α1t α2tπ ( ˆ , ˆ ) < 0

2. Understanding Why?

∂Q(µ)∂µ

=Margisnal

¸v¸alu

< δ =ut(π)

s ¸ ¸ x

=Marginal Loss

) =⇒ realizing loss is costly if ∆µ is small or πt < 0 is large in magnitude.

) Note If shifted

Gain =

∂Q(µ)

∂µ × (α2t −

α1t ) ˆˆ

Loss = δπt

Optimal Policy

1. Result 3: Loss-Holding Region Increases in α̂1t) Why? Relative gain from shifting ( ˆ − ˆ ) decreases as ˆα2t α1t α1tincreases

2. Result 4: Policy For Gains)

α2t α1tIf Q ( ˆ ) < ˆ , hold gains if greater than some

∗ α1t α2tπ ( ˆ , ˆ ) > 0

)α2t α1t

If Q ( ˆ ) > ˆ , liquidate any gain.

) Why? Hold large gains in some cases as current gains reduces probability that πt+1 = πt + rit+1 < 0

3. Result 5: No Liquidation If Manager Is Better)

α1t α2ttNo liquidation is optimal if ˆ > ˆ for any given π ∈ R

)α1t α2t

Why? If ˆ > ˆ , then sticking with same manager is thebest chance to recover losses (given participation is satisfied)

Illustration Of Optimal PolicyFigure:Hold Losses Even if α1 < α2ˆ ˆ

Illustration Of Optimal Policy

Figure:Loss-Holding Region

Optimal Policy For Rational Investor

1. Objective: Mean-Variance Optimization

tω∈HR

.tˆ= max ω α t

γ2ωtΣω

2. Solution:ωi = α̂it

γσ2it

3. Discussion:) Simplification: General time consistent policy under learning

is complicated

) Lynch&Musto (2003): Similar simplification assumption with exponential utility and one-period investors

) Alternative: Assume exponential utility and one-period agents, so that policy of old and new agent coincide given information

Dynamics Of Investor-Base

Figure: Dynamics Of Investor-Base

› Sequence of poor performce =⇒ Higher fraction of Loss-Averse Investors in Fund

Equilibrium Fund Flows

Figure: Fund Flow Schedules

Alternative Theories1. Lynch & Musto (JF,2003):

) Optimal replacement of manager by company below a cut-off performance=⇒ Magnitude of shortfall has no information content)

) =⇒ asset demand similar below cut-off2. Berk & Green (JPE,2004)

) Decreasing returns to scale) Quantities (size of fund) adjust so that expected excess returns

on all funds are equalized to zero) Return chasing, differential abilities and lack of persistence are

all consistent with each other3. Lynch & Musto For Current Evidence?

) P(firing) and hence convexity decreasing in reputation) Consistent with empirics? Some manager firing even for ’Top’

category) =⇒ Some insensitivity should have been observed if firing

mechanism was true

Conclusions

1. Lack of Flow Convexity for Reputed Funds (or for 40% of Industry money)

2.No Risk Shifting For Top funds in response to Mid-Year rank

3.Some 2 nd half risk-sfiting for bad repute funds

4.Fund Flow heterogeniety could be explained through presence of loss-averse investors

Thank You !

apoorva javadekar -role of reputation for mutual fund flows

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